5. Let E be the solid region above the plane z = 2 and below the sphere ² + y² + z² = 16 (see diagram to the right). (a) Set up, but DO NOT EVALUATE, iterated integrals for dV (2 + + م( (1² + y² + z using cylindrical coordinates. Clearly show how how you obtained your limits of integration.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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5. Let E be the solid region above the plane z = 2 and below the sphere
z² + y? + 2? = 16 (see diagram to the right).
x.
(a) Set up, but DO NOT EVALUATE, iterated integrals for
تور
|(? + y? + 2?) dV
using cylindrical coordinates. Clearly show how how you obtained your limits of integration.
(b) You might be tempted to try spherical coordinates for this object. Carefully explain why bounds for p
and ø will depend on each other in this case.
Transcribed Image Text:5. Let E be the solid region above the plane z = 2 and below the sphere z² + y? + 2? = 16 (see diagram to the right). x. (a) Set up, but DO NOT EVALUATE, iterated integrals for تور |(? + y? + 2?) dV using cylindrical coordinates. Clearly show how how you obtained your limits of integration. (b) You might be tempted to try spherical coordinates for this object. Carefully explain why bounds for p and ø will depend on each other in this case.
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